Optimizing Injection Parameters of Multi-Stage Alternating Acid Fracturing with a Coupled Model of Acid Etching and Interface Tracking

Abstract Acid fracturing enhances hydrocarbon production in tight carbonate reservoirs by creating fracture conductivity through non-uniform acid-rock reactions along fracture walls. Multi-stage alternating injection in acid fracturing has been demonstrated to effectively enhance non-uniform acid etching by promoting the development of viscous fingering. To optimize the parameters of alternating injection, an acid fracturing model was developed that integrates alternating injection with a coupled acid-rock reaction and fluid interface tracking approach. The model determines the distributions of acid concentration, fluid viscosity, and leakoff coefficient using the interface tracking method, while changes in fracture width are computed via the acid-rock reaction model. A viscous fingering index is introduced to evaluate the effectiveness of alternating injection. A higher index indicates more pronounced viscous fingering and, consequently, more effective acid fracturing. The results reveal that the viscous fingering index increases with greater viscosity contrast. For a fracture width of 3 mm, pronounced fingering is observed with a viscosity contrast of 1:5 during two-stage alternating injection. The viscous fingering index initially increases with the number of alternating stages as the viscous fingers elongate. However, beyond a critical number of alternating stages, the number of viscous fingers decreases, indicating that an optimal number of alternating stages exists for a given fracture width. Additionally, it was observed that an optimal injection rate of low-viscosity acid exists for a given fracture width. Below this optimal rate, the viscous fingers remain short, resulting in a more uniform etching pattern. Conversely, when the injection rate exceeds the optimal level, the viscous fingers merge, diminishing the effectiveness of the non-uniform etching.